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High School Calculus Math Course Outline

High School Calculus Math Course Outline

1.0 Credit

This course includes a thorough study of differentiation and integration with many applications. Limits and continuity are investigated in-depth. The course will emphasize the importance of mathematics studied to date. After completion of this course, the student may wish to take the Advanced Placement Test.

1- Introduction & Review

  • Welcome to Calculus
  • Course Outline
  • Course Syllabus
  • Completing Math Assessments
  • Calculus On The Web
  • Review — Stuff You Should Already Know
  • Pretest
  • Assignment: Calculus Pretest

2- Limits & Continuity

  • An Introduction to Limits & Continuity
  • Quiz: Introduction to Limits & Continuity
  • Tangent Lines & Rates of Change
  • Handout: Tangent Lines & Rates of Change Worksheet
  • Assignment: Tangent Lines & Rates of Change
  • The Limit
  • Handout: The Limit Worksheet
  • Assignment: The Limit
  • One-Sided Limits
  • Handout: One-Sided Limits Worksheet
  • Assignment: One-Sided Limits
  • Computing Limits
  • Handout: Computing Limits Worksheet
  • Assignment: Computing Limits
  • Infinite Limits
  • Handout: Infinite Limits Worksheet
  • Assignment: Infinite Limits
  • Limits at Infinity
  • Handout: Limits at Infinity Worksheet
  • Assignment: Limits at Infinity
  • Continuity
  • Handout: Continuity Worksheet
  • Assignment: Continuity
  • Additional Resources
  • Handout: Limits & Continuity Exam
  • Assignment: Limits & Continuity Exam

3- Derivatives

  • Introduction to Derivatives
  • Definition & Interpretation of the Derivative
  • Handout: Definition & Interpretation of the Derivative Worksheet
  • Assignment: Definition & Interpretation of the Derivative
  • Differentiation Formulas
  • Handout: Differentiation Formulas Worksheet
  • Assignment: Differentiation Formulas
  • Product & Quotient Rule
  • Handout: Product & Quotient Rule Worksheet
  • Assignment: Product & Quotient Rule
  • Derivatives of Trig Functions
  • Handout: Derivatives of Trig Functions Worksheet
  • Assignment: Derivatives of Trig Functions
  • Derivatives of Exponential & Logarithm Functions
  • Handout: Derivatives of Exponential & Logarithm Functions Worksheet
  • Assignment: Derivatives of Exponential & Logarithm Functions
  • The Chain Rule
  • Handout: The Chain Rule Worksheet
  • Assignment: The Chain Rule
  • Implicit Differentiation
  • Handout: Implicit Differentiation Worksheet
  • Assignment: Implicit Differentiation
  • Related Rates
  • Handout: Related Rates Worksheet
  • Assignment: Related Rates
  • Higher Order Derivatives
  • Handout: Higher Order Derivatives Worksheet
  • Assignment: Higher Order Derivatives
  • Additional Resources
  • Handout: Derivatives Exam
  • Assignment: Derivatives Exam

4- Applications of Derivatives

  • What’s the Big Deal About Derivatives, Anyway?
  • Rates of Change
  • Critical Points & Extrema
  • Handout: Critical Points & Extrema Worksheet
  • Assignment: Critical Points & Extrema
  • The Shape of a Graph
  • Handout: The Shape of a Graph Worksheet
  • Assignment: The Shape of a Graph
  • The Mean Value Theorem
  • Handout: The Mean Value Theorem Worksheet
  • Assignment: The Mean Value Theorem
  • Optimization
  • Handout: Optimization Worksheet
  • Assignment: Optimization
  • Linear Approximations
  • Handout: Linear Approximations Worksheet
  • Assignment: Linear Approximations
  • Midtest
  • Assignment: Calculus Midtest
  • Handout: Applications of Derivatives
  • Assignment: Applications of Derivatives

5- Integrals

  • Working Backwards
  • Indefinite Integrals
  • Handout: Indefinite Integrals Worksheet
  • Assignment: Indefinite Integrals
  • Computing Indefinite Integrals
  • Handout: Computing Indefinite Integrals Worksheet
  • Assignment: Computing Indefinite Integrals
  • Substitution Rule for Indefinite Integrals
  • Handout: Substitution Rule Worksheet
  • Assignment: Substitution Rule
  • Area Problem
  • Handout: Area Problem Worksheet
  • Assignment: Area Problem
  • Definite Integrals
  • Handout: Definite Integrals Worksheetv
  • Assignment: Definite Integrals
  • Computing Definite Integrals
  • Handout: Computing Definite Integrals Worksheet
  • Assignment: Computing Definite Integrals
  • Substitution Rule for Definite Integrals
  • Handout: Substitution Rule for Definite Integrals Worksheet
  • Assignment: Substitution Rule for Definite Integrals
  • Integration by Parts
  • Handout: Integration by Parts Worksheet
  • Assignment: Integration by Parts
  • Partial Fractions
  • Handout: Partial Fractions Worksheet
  • Assignment: Partial Fractions
  • Improper Integrals
  • Handout: Improper Integrals Worksheet
  • Assignment: Improper Integrals
  • Additional Resources
  • Handout: Integrals Exam
  • Assignment: Integrals

6- Applications of Integrals

  • What’s the Big Deal About Integrals, Anyway?
  • Area Between Curves
  • Handout: Area Between Curves Worksheet
  • Assignment: Area Between Curves
  • Volumes of Solids of Revolution (Part 1)
  • Handout: Method of Rings Worksheet
  • Assignment: Method of Rings
  • Volumes of Solids of Revolution (Part 2)
  • Handout: Method of Cylinders Worksheet
  • Assignment: Method of Cylinders
  • Volume
  • Work
  • Handout: Work Worksheet
  • Assignment: Work
  • Assignment: Applications of Integrals

7- Sequences & Series

  • Sequences & Series
  • Sequences
  • Series: The Basics
  • Series: Convergence & Divergence
  • Special Series
  • Integral Test
  • Comparison Test
  • Alternating Series Test
  • Absolute Convergence
  • Ratio & Root Tests
  • Strategy for Series
  • Estimating the Value of a Series
  • Power Series
  • Taylor Series
  • Additional Resources
  • Post-Test
  • Assignment: Sequences & Series

8- Course Survey

  • Handout: Course Survey
  • Assignment: Course Survey
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